Question

Two objects, one 4 times as massive as the other, are approaching each other under their mutual gravitational

attraction. When the separation between the objects is 100 km, the acceleration of the lighter object is 1 m/
s2. When the separation between them is 25 km, the acceleration of the heavier object is​

Answer 1

To Find :

The acceleration of the heavier object.

Solution :

Force of gravitation on lighter object by heavier object is :

`F = (Gm(4m))/(100^2)`

Acceleration of lighter object is given by :

`a_s = (4Gm)/(100^2)\\\\m = (50^2)/(G)` .....1)

Now, acceleration of heavier object when separation between them is 25 km :

`4ma_h = (Gm(4m))/(25)\\\\a_h = (Gm)/(25)`.....2)

Putting value of m in equation 2, we get :

`a_h = (G* 50^2)/(G * 25)\\\\a_h = (2500)/(25)\\\\a_h = 100\ m/s^2`

Therefore, the acceleration of the heavier object is​ 100 m/s².